Initially $\kappa$-compact spaces for large $\kappa$

Christodoulou, Stavros. "Initially $\kappa $-compact spaces for large $\kappa $." Commentationes Mathematicae Universitatis Carolinae 40.2 (1999): 319-325. <http://eudml.org/doc/248413>.

@article{Christodoulou1999,
abstract = {This work presents some cardinal inequalities in which appears the closed pseudo-character, $\psi _c$, of a space. Using one of them — $\psi _c(X) \le 2^\{d(X)\}$ for $T_2$ spaces — we improve, from $T_3$ to $T_2$ spaces, the well-known result that initially $\kappa $-compact $T_3$ spaces are $\lambda $-bounded for all cardinals $\lambda $ such that $2^\lambda \le \kappa $. And then, using an idea of A. Dow, we prove that initially $\kappa $-compact $T_2$ spaces are in fact compact for $\kappa = 2^\{F(X)\}$, $2^\{s(X)\}$, $2^\{t(X)\}$, $2^\{\chi (X)\}$, $2^\{\psi _c(X)\}$ or $\kappa = \max \lbrace \tau ^+, \tau ^\{<\tau \}\rbrace $, where $\tau > t(p,X)$ for all $p \in X$.},
author = {Christodoulou, Stavros},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {initially $\kappa $-compact space; $\kappa $-bounded space; closed pseudocharacter; cardinal inequalities; initially -compact space; -bounded space; closed pseudocharacter for a space},
language = {eng},
number = {2},
pages = {319-325},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Initially $\kappa $-compact spaces for large $\kappa $},
url = {http://eudml.org/doc/248413},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Christodoulou, Stavros
TI - Initially $\kappa $-compact spaces for large $\kappa $
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 2
SP - 319
EP - 325
AB - This work presents some cardinal inequalities in which appears the closed pseudo-character, $\psi _c$, of a space. Using one of them — $\psi _c(X) \le 2^{d(X)}$ for $T_2$ spaces — we improve, from $T_3$ to $T_2$ spaces, the well-known result that initially $\kappa $-compact $T_3$ spaces are $\lambda $-bounded for all cardinals $\lambda $ such that $2^\lambda \le \kappa $. And then, using an idea of A. Dow, we prove that initially $\kappa $-compact $T_2$ spaces are in fact compact for $\kappa = 2^{F(X)}$, $2^{s(X)}$, $2^{t(X)}$, $2^{\chi (X)}$, $2^{\psi _c(X)}$ or $\kappa = \max \lbrace \tau ^+, \tau ^{<\tau }\rbrace $, where $\tau > t(p,X)$ for all $p \in X$.
LA - eng
KW - initially $\kappa $-compact space; $\kappa $-bounded space; closed pseudocharacter; cardinal inequalities; initially -compact space; -bounded space; closed pseudocharacter for a space
UR - http://eudml.org/doc/248413
ER -